1. Field of the Invention
The present invention relates to methods and apparatuses for spectrum analysis and encoding and decoding data.
2. Description of Related Art
In monostatic pulse sounding, creation of many samples in a relatively short time is often needed because the signal-to-noise ratio may be very poor or the signals have large Doppler frequencies due to the fast movement of the reflector. Complementary pulse or Barker codes have been used for those conditions; but their use is limited if the Dopplers are very high. If, in addition, echoes from short ranges can occur simultaneously with large ranges, these phase-coded pulse sequences can not be used to increase the number of samples for signal-to-noise ratio improvement.
In this case, another unevenly spaced phase code, the staggered pulse code is proposed. We have developed a staggered pulse code which provides 128 phase-coded samples in the time space of two equally spaced pulses. In the spectral domain, however, the staggered pulse code has only a very limited dynamic range due to the cross-talk between the ranges and the leakage of any frequency into other spectral channels. This is already true for the complementary pulse or the Barker codes if there is a large Doppler present. Even in standard spectrum analysis of equally spaced samples, the sin x/x properties of the method limit the dynamic range. It has been overcome by filtering; but this process widens the spectral lines and decreases signal-to-noise.
In coherent radio or acoustic Radar and in ionosondes, the expected echoes in each range bin are coherent and are limited in number. In those applications, the noise often consists of a limited number of coherent interferers with a limited bandwidth, smaller than the pulse bandwidth. Many methods have been developed, like the Maximum Likelihood Method (MLM) (J. Capon (1969), “High-resolution Frequency-wave-number Spectrum Analysis”, Proc. IEEE, v 57, p. 1408-1418.), the Maximum Entropy Method (MEM) (J. P. Burg (1967) “Maximum Entropy Spectral Analysis”, paper presented at 37th Annual International SEG Meeting, Oklahoma City, Okla., and reprinted in “Modem Spectrum Analysis, edited by Donald G. Childers, IEEE Press.), and MUSIC (R. O. Schmidt (1981), “A Signal Subspace Approach to Multiple Emitter Location and Estimation”, Ph.D. Dissertation, Stanford University.) which have been described in several books (E. R. Kanasewich, “Time Sequence Analysis in Geophysics”, 3rd Edition (1981), The University of Alberta Press; S. M. Kay, “Modem Spectral Estimation”, (1998), Prentice Hall, Engewood Cliffs, N.J.; R. W. Hamming, S. Haykin, Editor, “Advances in Spectrum Analysis and Array Processing”, Prentice Hall Advanced Reference Series). On the subject, several patents have been awarded. The most relevant have been referenced here. In particular, in U.S. Pat. No. 4,613,978, narrow band interference suppression is proposed by cutting out large amplitudes in the spectrum. This method, as all the mentioned mathematical solutions which use computer time consuming matrix inversion, disregards the phase of signal and interference and work on the power spectrum.
Most of the data from ionosondes and other coherent Radars are organized in 3- or 4-dimensional displays with frequency on the horizontal axis and range on the vertical axis. To make those displays readable, only a limited number of ranges can be occupied by data. Any range can just display an amplitude and an identifier (Doppler, Polarization or incidence angle). Unfortunately, conventional spectral analysis has not produced effecient methods for optimizing the signal-to-noise ratio under these conditions.